Mean hatching success across all females (n = 352 females) was 17 ± 1.2% with a wide range of variation (0–87.8%). There was a significant effect of sire (F19,40 = 1.98, P < 0.05, Cohen's standardized effect size (Cohen, 1988), d = 0.484) on the proportion of eggs that hatched, suggesting the presence of significant genetic variance for embryo viability (Fig. 1). The dam effects were not significant (F40,40 = 0.58, n.s., d = 0.381). The genetic incompatibility hypothesis predicts that embryo viability depends on an interaction between sire and dam genotypes. Thus, hatching success should vary less across a male's mates when they are from a similar genetic background than when they have relatively greater genetic variability. Thus, the within subject variance in hatching success for sons mated to three unrelated full sibling females should be lower than for their brothers mated to three unrelated females. The within subject effect of female relatedness group was not significant (F1,40 = 1.55, n.s., d = 0.098). Critically for distinguishing between the intrinsic male quality and the incompatibility hypotheses, the sire by female relatedness group interaction was not significant (F19,40 = 0.78, n.s., d = 0.304). We also calculated the standard deviation of the hatching success of males mated to females in each relatedness group. The genetic incompatibility hypothesis predicts that the standard deviation in hatching success should be significantly lower for males mated to groups of females who are sisters compared with males mated to groups of unrelated females, because the later should have greater genome wide variability. Again, there was no significant difference in standard deviation between female relatedness groups (the mean ± SE standard deviation across sisters was 17.37 ± 1.79 and across unrelated females was 18.03 ± 1.79; F1,40 = 0.07, n.s., d = 0.024), and again the interaction term between sire and female relatedness group was not significant (F19,40 = 0.74, n.s., d = 0.343).
Patterns of genetic variance in hatching success were assessed from the average hatching success attributable to each son across his different mates, regardless of female relationship group. The genetic analysis was thus fully balanced with two sons per dam family, and three dams per sire. Variance components were extracted from a nested analysis of variance with sire as the main effect and dams nested within sires as a random factor (Becker, 1984). As in our full analysis, there was a significant effect of sire (F19,40 = 2.015, P < 0.05) and no significant effect of dam (F40,60 = 0.613, n.s.) on the average hatching success across a male's mates. The narrow sense heritability of hatching success was 0.46 ± 0.29. Coefficients of variation were calculated following the method proposed by Houle (1992). There were high levels of additive genetic variation (CVA = 21.10), residual variation (CVR = 58.86), and total phenotypic variation (CVP = 62.53). Sperm viability could not account for the observed variability in hatching success. Sperm viability was high (84.4 ± 0.5% live sperm, range 61–96%) and sire family mean sperm viability did not predict sire family mean hatching success (F1,13 = 0.02, n.s.). However, accessory gland products could influence the observed patterns in hatching success. There was a strong and significant sire effect on male investment into the accessory glands (F19,37 = 2.16, P < 0.05, d = 0.655), the narrow sense heritability being 0.85 ± 0.55 (CVA = 11.08, CVR = 21.30, CVP = 24.01). Moreover, there was significant sire covariance between hatching success and accessory gland weight (nested ancova, F19,43 = 4.18, P < 0.0001) and a significant correlation between the sire family means of these traits (+0.662, n = 20, P < 0.01; see Fig. 1). The sire family mean correlation provides a conservative estimate of the underlying genetic correlation (Lynch & Walsh, 1998). Using the ancova method (Becker, 1984) the estimate of the genetic correlation was 0.793 ± 0.452. There was no genetic variance due to sire for either soma weight (calculated as body weight minus the sum of the weights of the testes and accessory glands) or testes weight (soma weight: F19,37 = 0.89, n.s.; testes weight: F19,37 = 1.06, n.s.), in agreement with previous results (Simmons, 2003). Moreover, the sire effect on male investment into the accessory glands (F19,37 = 2.49, P < 0.01, d = 0.696) and the significant covariance between hatching success and gland weight (F19,42 = 3.19, P < 0.001) persisted when soma weight was entered into the analyses as a covariate.